The Fate of excited state of ⁴He

We investigate the properties of the excited state of $^4\mathrm{He}$, $^4\mathrm{He}^*$, within the framework of Efimov physics and its connection to the unitary point of the nuclear interaction. We explore two different approaches to track the trajectory of $^4\mathrm{He}^*$ as it crosses the $^3\mathrm{H}$+p threshold and potentially becomes a resonant state. The first approach involves an analytical continuation of the energy with respect to the Coulomb coupling, while the second approach introduces an artificial four-body force that it is gradually released. By utilizing Pad\'e approximants and extrapolation techniques, we estimate the energy and width of the resonance. Our results suggest a central energy value of $E_R=0.060(3)$ MeV and a width of $\Gamma/2=0.036(6)$ MeV using the Coulomb analysis, and $E_R=0.068(1)$ MeV and $\Gamma/2=0.007(5)$ MeV with the four-body force analysis. Interestingly, these results are consistent with calculations based on {\it ab-initio} nuclear interactions but differ from the accepted values of the $0^+$ resonance energy and width. This highlights the challenges in accurately determining the properties of resonant states in light nuclei and calls for further investigations and refinements in theoretical approaches.